old-racket-sicp-solutions/exercise-1.07-different-good-enough-function.rkt

#lang racket
(define (square x) (* x x))
(define (avg a b) (/ (+ a b) 2))

(define (improve-guess x guess)
  (avg (/ x guess) guess))

(define (epsilon-square-root x guess)
  (abs (- (square guess) x)))

(define (precision-sufficient x guess precision)
  (< (epsilon-square-root x guess) precision))

(define (precision-sufficient-two x guess precision)
  (<
   (abs (- guess (improve-guess x guess)))
   (abs (* guess precision))))

(define (sqrt-iter guess x precision)
  (if
   (precision-sufficient x guess precision)
   guess
   (sqrt-iter (improve-guess x guess) x precision)))

(define (sqrt-iter-two guess x precision)
  (if
   (precision-sufficient-two x guess precision)
   guess
   (sqrt-iter-two (improve-guess x guess) x precision)))

(sqrt-iter 2.6 7 0.000001)